the first rule airplay is if you're having issues, reboot your router. (it depends very heavily on a stable network)
the second rule of airplay, is don't use it unless you absolutely have to.
if it's playing fine on your phone, but not making it to the TV, it's probably a network issue.
--to avoid confusion, if using airplay, please say "airplay to TV." if you say "cast to TV" that normally means using the TV manufacturer's casting software, or google cast, which is different troubleshooting.
--if you're at the far end of your house from your router and have low signal, you might have issues, since the wireless has to make 2 jumps over a poor connection.
--You say you tried files and VLC, both on the phone?
have you tired VLC on the appleTV? you'll have to share a folder from your Mac using windows file sharing, but you can play directly on the aTV
Don't use the online convertor, get handbrake, and do it locally. It also has presets pre-made for apple products, so you'll know they work.
you also seem to be doing a ton of steps, and making this way more complicated than it really needs to be.
And probably having a lower quality experience, than if you did it one of the "easier" ways.
If you don't need your phone involved, don't use it.
If you're trying to play your own files back, and don't mind having the computer on when you're trying to watch, there are 3 options, (maybe more). All are free, but there are paid upgrades that give you more features. They'll also probably give you better quality playback, Since the files are actually playing on the aTV, it's able to buffer a bit ahead, so it can cover for network hiccups a lot better than airplay.
from end user experience lowest to highest, those are VLC, Infuse, Plex
Infuse and plex will both give you a "Netflix like" experience
Plex supports playback on the most devices, it's available on most smart TVs and streaming devices.
VLC - will allow you to access network shares
Infuse, - will access network shares, but it can also automatically tag and organize movie and TV shows. This all happens on the aTV, if you've got multiple devices, it can share the library across them, but it can be a little clunky.
Will play most files directly, but for some, you'll need the paid upgrade.
Plex - Runs a server on your computer (windows, Mac, Linux, or even some network hard drives), you then get a client program ( computer, iOS, appleTV, android, most other smart TVs or streaming devices, and also any web browser)
You don't have to worry about sharing folders, as the sever will read the files locally, and then share the files itself.
The server will auto tag all your files.
If you go to watch something that can't be played by the device you're watching on, the server will convert as you watch (so you'll need a moderately powered computer)
The server automatically securely shares to the internet, as long the connections at your home and wherever your phone are fast enough, you can watch your library anywhere with an internet connection.
If you want, you can also share with friends, they make their own account, and you add them, they also can watch anywhere.
also with the paid upgrade, you can sync to your phone,
Both plex and infuse will keep track of what you've watched, so if you're in the middle of binging a show, the next episode will be right at the top ready to go.
You can also stop playback on one device, and pick up in the same place on another.
